"There is plenty of capacity on our weekend trains, and we'd be happy to fill those seats with families and others traveling in and out of Boston this summer," Luis Manuel Ramirez, the MBTA general manager, said in a statement.

"With this special fare, our goal is to offer a price that is highly competitive with the cost of driving and parking, and we look forward to seeing the results of this pilot," said David Scorey, the head of Keolis, which has the contract to operate the commuter rail for the MBTA.

Current weekend ridership estimates come in at 16,600 trips on Saturday and 9,000 trips on Sunday. That adds up to roughly five to 10 percent of weekday ridership.